A cylinder has inner and outer radii of $6 cm$ and $12 cm$ , respectively, and a mass of $1 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $15 Hz$ to $9 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-08-05T19:30:00

The change in angular momentum is $=0.34kgm^2s^-1$

The angular momentum is $L=Iomega$

The mass of the cylinder is $m=1kg$

The radii of the cylinder are $r_1=0.06m$ and $r_2=0.12m$

For the cylinder, $I=m(r_1^2+r_2^2)/2$

So, $I=1*(0.06^2+0.12^2)/2=0.009kgm^2$

The change in angular velocity is

$Delta omega=Deltaf*2pi=(15-9)*2pi=12pirads^-1$

The change in angular momentum is

$DeltaL=I Delta omega=0.009*12pi=0.34kgm^2s^-1$

A cylinder has inner and outer radii of 6 cm6 cm and 12 cm12 cm, respectively, and a mass of 1 kg1 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 15 Hz15 Hz to 9 Hz9 Hz, by how much does its angular momentum change?